"Paires et Séries," a stirring exhibition at Centre Pompidou here in Paris shows Matisse to have been someone who tried always to stretch himself, representing the world in the truest possible way, as he saw it, which meant that the truth, or the representation of it, was different depending on the moment in which it was captured. Everything was true and everything changed, and visual truth was, of course, elusive.

That means Matisse didn't see anything the same way twice, which is why this gathering of paintings – from the Pompidou collection itself, with borrowings from museums and private collections in France and from Russia, the U.S., Britain and other countries – is more than a life-survey of a great artist. It's an attempt to get at what Matisse himself was trying to do in his works: see clearly from different angles, from different times and different frames of mind using paintings of similar or the same subjects that were created within days or months of each other.

Matisse inevitably draws crowds who admire his graceful lines and fauvist tints. But he is also one of those artists whose beautiful paintings belie the seriousness of his efforts at trying to comprehend and visualize how things are perceived or represented.

Take two of the paintings paired here. The first, Interieur, bocal de poissons rouge, from 1914, shows two goldfish in a large jar, at the center of the canvas, before a window that takes up the bulk of the right side of the frame.

The jar with the fish is echoed in the forefront with a view of the top of a pot of some sort on a table, its green and yellow surface suggesting the greens and yellows of the scene outside the window, a window that is angled from the viewer's perspective. The table on which the jar sits is shown at an angle to the viewer too, but it juts out slightly from the window, creating a sense of interior space and three-dimensionality before the flat expansive depth of the landscape.

At the rear of the room square pillows, limned in orange and yellow rest in nestled diamonds on a couch at the back of the frame. The eye is directed toward the vanishing point through the window, toward a space just beyond a building – sketched in yellow and bluish gray that echoes the color of the base of the window (whose sill is deep orange, like the tiny flower pot on the table where the jar with the goldfish sits, like the outline of the pillows). This is a moment of day, with the light falling just so, the shadows marking the objects just so, this encounter with the day through a fleeting prism.

Everything, every shape, every color, suggests another, suggests a blink of what we can make out: our eyes need to focus carefully on the scene to see how the angles, the shades, the directions of the surfaces reveal a world of depth and indirection and wonderful airy texture sprung from the captured luminosity of the day within and without. You get a sense of moment held in a numinous clarity of transparent light. Matisse is saying, "I will show you time in a mote of dust."

Next to it, from 1914-15, is the similar but different Poissons rouges et palette, which also has a jar with two goldfish placed on a table near the center of the frame. Beside the jar is a single orange, rather than a small orange pot, and instead of showing the street from the perspective of the apartment, Matisse forces on us the surfaces within the interior – a table, another table, a floor, a wall, a flatness shingled on the canvas as if reality were a shuffling of visual playing cards.

Matisse presents claustrophobia here; the viewer himself watches the scene from a constricted space, a virtual jar that does not permit a 360-degree view but a blinkered perspective – gravity without expanse.

Here, the immobility of the scene – the way it forces the viewer to look "within" without a sense of escape into a luminous background as in the other painting with which it's paired – renders cool the palette: shadows given a glimmer of light, an artistic gleam. It's like a semi-cubist half self-portrait, with fragments of "things" representing an artist's point of view: the suspended fish in a flattened jar, the hint of the painter's arm or hand or brush at the right, the interiority of perception and the exteriority of depiction.

Or consider two paintings from two decades later: Les Marguerites, from July 1939, and Liseuse sur fond noir, from August 1939. In the first painting, a woman, sketched in black on a red quadrant, is seated at the bottom left of the frame. She rests her chin on her left hand while her right is nestled in her lap. Above her is a painting of a woman seated or lying in the opposite direction, in pink and white. To the "red" woman's left is a table on which sits a Grecian urn, and a vase of daisies (marguerites), with lemons scattered around the two objects. The table on which the vase and urn sit is a sort of pedestal.

The images here are flattened: the woman is like a collage cutout, the table has the illusion of depth without depth, the daisies pressed against the plane of the picture.

The other picture, Liseuse sur fond noir, or "woman reading against a black background," has the elements of the earlier painting – a seated woman, a vase of daisies, a painting within the painting, a black background. But the woman here is given more three-dimensional depth – she is rendered as a figure rather than outlined in black, her head resting on her left hand as she reads something that's been placed on a pink table whose surface has been tilted toward the viewer. An aquamarine vase of exuberant daisies sits on the table; behind it is a canvas of a standing figure, sketched in black on a white background. Other small canvases or sketches are affixed to the black wall behind. The woman and the daisies are reflected in a yellow-framed mirror behind, so we see her elbow twice, the daisies, slightly altered in the reflection, twice, a tricky vanishing point of depth perception on a two-dimensional plane.

You see how Matisse plays with the depiction of the geometry of interior space in these two paintings, and of the figures inhabiting them: we can fade into the background or be part of the texture of a scene; the eye can place elements within a frame in a way that refracts reality.

The other pairs, the other series here, explore light, color, shape – everything we can see, everything we can try to visualize. Matisse worked and reworked, sketched and re-sketched, like a writer trying to get to the perfect phrase. The perfect visualization is impossible, as he knew – but the attempt is close to perfection.

Because Matisse worked here so carefully at exhibiting different visual sensations, it's worth taking in this exhibition as slowly as possible (difficult enough given the crowds, but worth the effort). These side-by-side pairings illuminate the artist's preoccupation with space, surface, depth, scale and the emotive possibility of color. Matisse's figures are often still against a supposedly still background; they seem silent, but they speak volumes.

The exhibition will travel to Copenhagen's Statens Museum for Kunst in July, then to New York's Metropolitan Museum of Art in December.